Performance of Partially Submerged Propellers 



to the right, facing forward. The origin is at the intersection of the shaft axis 

 with the transverse propeller plane. The coordinate system is shown in the 

 upper part of Fig. A3. Arrowheads indicate the positive x, y, and z directions. 

 Also included for reference are the positive direction of rotation n and speed v 

 for a right-hand propeller. 



a y 



Fig. A3 - Coordinate system and force diagram 



Eccentric application of the thrust force T at a distance y below the shaft 

 produces a moment M = Ty. This moment can be represented by a pure moment 

 in the vertical plane (z = 0), M^ and a vertical force F^ applied to the shaft in 

 the same transverse reference plane, see Fig. A3. Resisting moments are gen- 

 erated at Plane A and Plane B, respectively: 



- M^Y = M^Y - F^ b , 



- "^BY = ^ZY - Fv b - F^ a . 

 From these relationships, the force f is 



Fv = (MbY - May)/3 



and the moment m, is 



- M7Y = [(a+ b) M.y - b Mgyl/a - 



1487 



